Research on conceptual understanding
Just an interesting piece... a recent study has found that teaching conceptual understanding in math makes children learn better, as opposed to teaching procedures.
You Do The Math: Explaining Basic Concepts Behind Math Problems Improves Children's Learning
The children were taught about solving equations such as
4 + 5 + 3 = ___ + 3
either procedurally, or conceptually. Procedural instruction went kind of like this:
"Add the three numbers on this side, 4 + 5 + 3. That's 12. Then subtract the number here from that, 12 - 3 = 9. That's the number that goes to the blank."
In the conceptual group they were taught about equivalence, the equation having two sides that have to be equal.
Of course... the conceptual teaching is the way to go!
Here's a link to the research paper (in press):
Matthews, P. & Rittle-Johnson, B. (in press). In pursuit of knowledge: Comparing self-explanation, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology.
You Do The Math: Explaining Basic Concepts Behind Math Problems Improves Children's Learning
The children were taught about solving equations such as
4 + 5 + 3 = ___ + 3
either procedurally, or conceptually. Procedural instruction went kind of like this:
"Add the three numbers on this side, 4 + 5 + 3. That's 12. Then subtract the number here from that, 12 - 3 = 9. That's the number that goes to the blank."
In the conceptual group they were taught about equivalence, the equation having two sides that have to be equal.
Of course... the conceptual teaching is the way to go!
Here's a link to the research paper (in press):
Matthews, P. & Rittle-Johnson, B. (in press). In pursuit of knowledge: Comparing self-explanation, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology.
Comments
I was also intrigued by what Keith Devlin wrote about the Davydov curriculum, but I'm having trouble finding much information about the actual activities he used or the progression of ideas. I really don't want to have to construct everything from scratch, and it sounded like they had a good system going---if I could just find out what it was...
I find the conclusions rather ridiculous though, of course children learn better when taught the concepts behind the math, vs. just the procedure. Would you say rote, mechanized, prodedural math is really learning? I wouldn't. I was taught that way and I want to give my kids more than "because I said so" or "because that's just the way we do it, now stop asking why." ;o) So I'm digging in and learning what I should have been taught yrs ago.
Ok, one more thing, I just have to say I am stunned that this had to be researched.
OK, vent over. :-D
OH, before I go I wanted to say that I just discovered your blog and will have to dig in and see what all you have. I LOVE living math and am looking for any helps in taking the concept beyond basic, intro math.
Have a wonderful day!
Gin